Safety Guarantees for Planning Based on Iterative Gaussian Processes
This work addresses the lack of guarantees in approximation methods for iterative GP predictions, providing a solution for researchers and practitioners in control and learning who need reliable uncertainty estimates for safety-critical applications.
The paper tackles the problem of analytically intractable uncertainty in iterative, multi-step predictions with Gaussian Processes (GPs) by deriving formal probability error bounds, guaranteeing that GP trajectories lie within specified regions with at least a probability of 1-ε for a given tolerance ε>0. It experimentally verifies that this method correctly tracks predictive uncertainty and demonstrates its application in safe reinforcement learning to verify and synthesize provably safe controllers.
Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable problem. While approximation methods exist, they do not come with guarantees, making it difficult to estimate their reliability and to trust their predictions. In this work, we derive formal probability error bounds for iterative prediction and planning with GPs. Building on GP properties, we bound the probability that random trajectories lie in specific regions around the predicted values. Namely, given a tolerance $ε> 0 $, we compute regions around the predicted trajectory values, such that GP trajectories are guaranteed to lie inside them with probability at least $1-ε$. We verify experimentally that our method tracks the predictive uncertainty correctly, even when current approximation techniques fail. Furthermore, we show how the proposed bounds can be employed within a safe reinforcement learning framework to verify the safety of candidate control policies, guiding the synthesis of provably safe controllers.